Răspuns:
[tex]\bf \purple{a = 4}[/tex]
[tex]\bf \red{b=1}[/tex]
Explicație pas cu pas:
[tex]\bf \dfrac{a+b}{2a-b} =\dfrac{5}{7} \implies 5\cdot(2a-b)=7\cdot(a+b)[/tex]
[tex]\bf 10a-5b=7a+7b[/tex]
[tex]\bf 3a-5b=7b[/tex]
[tex]\bf 3a=7b+5b[/tex]
[tex]\bf 3a=12b~~~\bigg|:3[/tex]
[tex]\bf \underline{a=4b}[/tex]
Aflam valoarea lui a si a lui b
[tex]\bf 5\cdot(2\cdot4b-b)=7\cdot(4b+b)[/tex]
[tex]\bf 5\cdot(8b-b)=7\cdot 5b[/tex]
[tex]\bf 5\cdot 7b=35b[/tex]
[tex]\bf 35b=35b~~~\bigg|:35[/tex]
[tex]\bf \red{\underline{b=1}}[/tex]
[tex]\bf a = 4\cdot 1\implies \purple{\underline{a = 4}}[/tex]
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